Question

If $\sin \theta = \cos \theta$, $0 \leq \theta \leq 90^\circ$, then the value of $\theta$ will be:

• A. $60^\circ$
• B. $45^\circ$
• C. $30^\circ$
• D. $0^\circ$

Hint:

Remember that $\sin \theta = \cos \theta$ always holds true when $\theta = 45^\circ$ in the first quadrant.

Answer 1

The Correct Option is B

 

Step 1: Given condition 
We are given $\sin \theta = \cos \theta$. 
 

Step 2: Divide both sides by $\cos \theta$ (valid for $0^\circ \leq \theta \leq 90^\circ$, except $\theta=90^\circ$) 
\[ \frac{\sin \theta}{\cos \theta} = \frac{\cos \theta}{\cos \theta} \] \[ \tan \theta = 1 \]

Step 3: Solve for $\theta$ 
\[ \tan \theta = 1 \,\Rightarrow\ \theta = 45^\circ \]

Step 4: Check interval 
Since $0^\circ \leq \theta \leq 90^\circ$, the only solution is $\theta = 45^\circ$. 
\[ \boxed{\theta = 45^\circ} \]